Why does Katarina get to keep her full reset when Yi lost his

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LOL

what is zhonya's

Are you trolling

During which she isn't dealing damage, moving or doing anything except not taking damage. Which gives her Shunpo time to get off cooldown but also allows her foes time to get CC cooldowns back and ready to use.

As opposed to AP Yi who becomes targetable again, after he's already gotten the penta. Not to mention he could also build Zhonya's.

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Kat has access to Zhonya's, is manaless, and can also hop escape instantly over walls without flash, also has damage reduction, and a healing debuff in case you tried to tank her

Remind me why Yi's was removed again when Kat's wasn't

Because Yi's untargetability dash hits up to 4 people and has its cooldown naturally lowered just by autoattacks. Yi also has extreme healing + defence if he manages to dodge your CC, and a good true damage on hit to go with his ults movement and attackspeed and his passive.

Kat can't do anything while under zhonya except wait to get surrounded, plus her CD reset does not affect that. In addition: Kat might have grave wounds, but so can any other AP user with morellicon. Yi can still heal unlike kat. Lee sin can also hop over walls, along with other champions. I do think Kat shouldn't get 15 sec CD removal for assits though.